NEW YORK (AP) — Maybe it's a cliché to say the gloves came off in Tuesday's presidential debate. But then again, maybe not, since the candidates sometimes looked like they were actually about to start boxing.

It was a tense and testy exchange at New York's Hofstra University, featuring a newly energized and forceful President Barack Obama squaring off against a vigorous, stand-your-ground Mitt Romney. But the evening will also be remembered for giving the distinct impression that these candidates were liking each other less and less.

—"I thought they were going to come to blows at one point," said Jonathan Paul, director of debate at Georgetown University.

—"It looked like they were circling a boxing ring," said Lillian Glass, a body language coach in Los Angeles.

—"I started thinking, here comes the Secret Service," quipped Jerry Shuster of the University of Pittsburgh.

One thing was clear: It was a distinctly different Obama than the one who gave a largely listless performance in the first debate. And there were differences, too, between Tuesday night's Romney and the more obviously confident one from the Denver debate.

Some impressions and assessments from analysts of political communication:

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THE PRESIDENT LEARNED HIS LESSON

First, the obvious: This time around, Obama was unquestionably more forceful, aggressive and effective than before — all words that were used to describe challenger Romney in the first debate.

Want more adjectives? "He was more direct, detailed, engaged and focused," said Kathleen Hall Jamieson, a professor of political communication at the University of Pennsylvania. "Stylistically, there are cues that suggest leadership. Obama had them."

For Glass, the body language coach in Los Angeles, it was a simple result of Obama having learned his lesson. "He really learned well from his mistakes," she said.

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A FREEING FORMAT

Another reason for the president's vastly improved performance was the format, some said. Obama appeared more comfortable with the town hall model — one that allowed him to engage with his questioners in the audience and roam around the stage, something he's good at. The lack of a desk or podium freed him, said Shuster: "He was very smooth in his ability to move around the floor."

As for Romney, though he gave as good as he got for much of the debate, "He seemed overanxious, ready to jump off his chair," Shuster said. "He seemed overanxious to make an argument."

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HOW AGGRESSIVE IS TOO AGGRESSIVE?

There's a fine line between aggressive and rude, and it was approached at times.

"You'll get your chance in a moment. I'm still speaking," Romney said crisply when Obama was in mid-sentence at one point, evoking some gasps in the audience.

"This was on the line — it was the president of the United States," said veteran Hollywood publicist Michael Levine. "I mean, WHOA. It was very forceful, on the other hand." Levine felt the debate was a draw, between "two men, both very bright, very articulate, very earnest."

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THE LIBYA MOMENT

Romney seemed to be waiting for the Libya question. And he was ready to pounce when an audience member asked about the terror attack that killed the U.S. ambassador to Libya in Benghazi.

Romney said it took Obama a long time to admit the episode had been a terrorist attack, but Obama said he had said so the day after in an appearance in the Rose Garden. Moderator Candy Crowley of CNN agreed, saying the president had in fact done so. Obama replied, "Say that a little louder, Candy."

Romney had a point in that while Obama did refer to terrorism the day after, some in his administration repeatedly linked it to protests over an anti-Islamic video and took almost a month to acknowledge those protests never occurred. And the administration hasn't explained why it took so long for that correction to be made or how it came to believe that the attack evolved from an angry demonstration.

Still, the exchange about it appeared to hurt Romney going forward. "He seemed rattled after that," said Paul, the Georgetown coach.

Jamieson agreed. "Romney had trouble getting his footing back for a while."

Even worse for him, though, Jamieson said, will be the inevitable fallout from the exchange being played again and again on TV.

"There's the debate, and then there's the battle of control for the news agenda afterwards," she said. "This is the sound bite likely to be played, and every time it is, it will disadvantage Romney."

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THE POLITICS OF FASHION

Some would say the candidates switched roles in terms of their debate performance; what's objectively true is that they switched tie colors, with Obama wearing red this time and Romney wearing blue. Is red warmer? Is blue cooler? Michelle Obama and Ann Romney, meanwhile, ignored both of those colors and turned heads by wearing the same shade of hot pink (likely a nod to October being breast cancer awareness month).

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THE COMEDY QUOTIENT (OR IS 'BINDER' THE NEW BIG BIRD?)

There were a few amusing exchanges in the earlier debates, but the extremely tense nature of this one seemed to preclude that possibility. There wasn't really a "Big Bird" or a "malarkey" moment, and even Joe Biden would have found little to chuckle about.

But Big Bird may have ceded way in our pop-culture consciousness to a brand new expression: "Binders full of women."

It came when Romney was answering a question about fair pay for women. While Obama mentioned the Lilly Ledbetter Fair Pay Act, which he signed into law, Romney spoke of his efforts to hire women into his cabinet when he was Massachusetts governor. He said he asked women's groups to help and, he said, "They brought us whole binders full of women."

Within moments, of course, social media pounced with multiple Twitter hashtags and a meme that featured a widely circulated image of women in a loose-leaf binder.

As for Obama, his best comedy moment may have come, fittingly for the night, in the form of a dig.

Romney asked him if he had looked at his pension lately. Obama parried: "I don't look at my pension. It's not as big as yours, so it doesn't take as long."

The crowd broke the rules and laughed. Score one for the president. And look for a rematch on pensions, binders and maybe even a return of Big Bird when the two meet again next Monday. If the feisty, aggressive versions of both candidates turn up again, it'll be fun to watch.